images of result of collaboration with Theodore Spyropoulos of minimaforms and part of the conceptual revisiting / reintepretation of project 19 by David Green, archigram. read more on L.A.W.u.N*project#20.

Images from simplistic implementation of the Octree algorithm in Maya. Primarily as an exercise to understand its API and class derivation within it.

BSP"Binary space partitioning (BSP) is a method for recursively subdividing a space into convex sets by hyperplanes. This subdivision gives rise to a representation of the scene by means of a tree data structure known as a BSP tree."

Octree"An octree is a tree data structure in which each internal node has up to eight children. Octrees are most often used to partition a three dimensional space by recursively subdividing it into eight octants."

Approximate Nearest Neighbour"Computing exact nearest neighbors in dimensions much higher than 8 seems to be a very difficult task. Few methods seem to be significantly better than a brute-force computation of all distances. However, it has been shown that by computing nearest neighbors approximately, it is possible to achieve significantly faster running times (on the order of 10's to 100's) often with a relatively small actual errors. ...."

Even accounting for the amateur nature of our attempt, it would appear that the above holds true in 3 dimensions as well ie. an octree algorithm provides a significant advantage over brute calculation of distances only when the point distribution is sparse, point sets are large (above 50000) and some tolerances are allowed in terms of measurement.

By now ancient sketch script a single NURBS with 3 dimensional components. It translates the world space coordinates of the component object into the moving-space defined by the ortho-normal vectors of the surface.

Differential_geometry_of_curves[Accessed May 2006]Frenet Vectors."A Frenet frame is a moving reference frame of n orthonormal vectors which are used to describe a curve locally at each point. It is the main tool in the differential geometric treatment of curves as it is far easier and more natural to describe local properties (e.g. curvature, torsion) in terms of a local reference system than using a global one like the Euclidean coordinates..."

Darboux_frame[Accessed May 2006]Darboux_frame:surface analogue to Frenet frame on a curve

swarms and distribution of intelligence: decentralised decision making

“That war (vietnam) also proved the self-defeating nature of centralization: the moreone tries to achieve total certainty, the greater the increase in the information flowneeded to run the operation, and therefore the more uncertain the final results. Farfrom solving the problem, computers ended up compounding it by producing theirown endless streams of information.” …

De landa, M. War in the Age of Intelligent Machine, (Cambridge: MIT Press, 1990)p. 79

self similarity and difference

Architecture as an assembly of design components implicitly suggests ‘self-similarity’ and ‘difference’ amongst the parts of the system. Particulars or aspects of this similarity and difference could be multitude. Nonetheless, our research aims to ‘appose’ and /or articulate the notion with other issues that deserve to be discussed. In recent ‘parametric’ systems of design and of codification of design for construction, this aspect of similarity and difference, have tended to be manifested in the production of ‘homeo-morphic’ geometries such as ‘adaptive (to curvature) tiling’ patterns, structural skins etc. Alternatively, there have been systems, like those in robotics , that concentrated on production of non-topological difference and on aspects of ‘family’ and ‘individual’ on the basis of ‘attributes’ such as constituent parts , specific task-capacities, transformation pathways etc.

Images and videos show attempts to combine the position & directional relations betweens 'objects in a swarm' and the morphological self-similarity of 'objects in a family', towards developing an formal language of at urban scale. This apart from more weathered concerns of architecture and urbanism including discourses on performance fitness, spatial perception and experience, socio-cultural implications etc.

This post is to acknowledge the influence on current work by ideas fostered directly under tutelage, and in association with Vasili Stroumpakos, Theodore Spyropolous, and James Warton. This inflection includes a critical area in design research: that of diagramming information towards the resolution of the 'data-cloud' that holds an architectural solution within.

notation systems: symbols and manipulation;

Marvin Minsky, pioneering extensive research in cognitive science, and evolution of intelligence, explicates that fundamental to the evolution of intelligence and problem solving capacities, is the need for a system of representation:

“All problem-solvers, intelligent or not, are subject to the same ultimate constraints–limitations on space, time, and materials. In order for animals to evolve powerful ways to deal with such constraints, they must have ways to represent the situations they face, and they must have processes for manipulating those representations.”

Extending the argument to the domain of ‘design-research’, it could be argued that symbols (notation) and operations (manipulations) are embedded within the ‘performative’ capacities and constraints of the selected tool (s) of design. They produce results, which extend beyond the level of affect and alter the sensibilities of the designer. They manifest themselves as shifts or variations in the organizational relationships and formal possibilities accessible to the designer. Further, symbol systems form an integral aid in ‘procedural thought’ argued for earlier, for any ‘problem-solving’ has to make creative leaps in the face of incomplete information regarding the problem. This because a notational system can be articulated at varying degrees of figural representation as well as describe immaterial substance, and the designer must construct or clarify the components to be examined. The use of notation is not only intended to make recognizable what was potentially unseen, rather to place emphasis on the components or elements of decided significance. In essence then, symbol-systems can aid the process of ‘pattern recognition’ within a ‘search’ for a ‘solution space’. The point here being that, these notations or symbols give data cognitive recognition, which down the path of ‘heuristic learning’ yield unique results based on their the selection . The research has to then clarify and codify its findings and discoveries to fuel its own pursuit further.

images and video relate to aforementioned 'diagramming' in so called non-CAD platforms, including Flash, maxMSP,external hardware and their digital controllers etc.

Photograph from FaceBreeder installation by Vasilis Stroumpakos and Theodore Spyropolous at AA School,London. Production Assistants included members from team Manifold, Reploy, YME etc.For more see facebreeeder.com

Last evening was the first public presentation of the computation and design group(co|de)at Zaha Hadid Architects. This group is an effort towards formulating a research unit within the office to address the following issues, and concerns.

Analytical computation, as an instrument to generate geometry and evaluate its ‘performance’, is inherently dependent on ‘meshes’ or node based geometry. The attempt on this short-term research was to understand the functioning of node-based geometry, text-based polygon file formats, types including Delaunay , Voronoi, half-space intersections, convex hulls etc.

In view of the lack of access to Maya's internal triangulation engines, the research concentrated on wrting simple translators to access external, command-line executables such as qhull,tetgen and surface evolver.Tetgen has so far proved to be most useful, in that it can be compiled into either an executable or a dll. ie. supports both standard MEL 'system' calls and c++ api calls from within Maya plugins. Further, tetgen also supports constrained delaunay triangulation.

Although resulting triangulated meshes do not support regular poly-modelling workflows, they provide interest as reference objects.They are also useful in geometric problem solving, eg: prim's algorithm.